Various projects are available in analytic number theory. These include questions on: distribution of primes, analytic properties of the Riemann zeta-function, explicit questions from elementary number theory (for example, every N>2 is the sum of a prime and a square-free number), and the distribution of primitive roots. See the Number Theory Group.

The interaction of the surfaces of spacecraft with the space environment has significant and poorly understood effects on the spacecraft's performance. In conjunction with UNSW Canberra Space, several projects are available investigating typical spacecraft surface interactions. Two particular targets for investigation are energy transfer and accretion processes in collisions with rarefied gasses, and understanding the factors controlling surface coating though photo-initiated polymerisation of adsorbates.

Quantum mechanics is the most accurate framework known for investigating and simulating chemical reactions, incorporating all significant physical effects in most cases. However, the practicality of using quantum mechanical descriptions of the dynamics of reactions is limited in practice by the computational cost of performing accurate quantum simulations.

Many applications exist for interrogating large, scattered, high-dimensional data sets to find a group of nearby points for an arbitrary test point. Examples range from advanced methods to simulate chemical reactions to facial recognition software. This project will develop fast neighbour searching algorithms and implementations with a focus on applications in chemistry and physics.

Suitable candidates will have a mathematical background suitable for applied mathematics research, and engage in scientific programming.

Gas-surface chemistry is vital to the functioning of technological society.  Reactions occurring on and with surfaces are pervasive in virtually all technological and industrial activities.  Being able to predict and thus engineer reactions at surfaces has profound importance to modern society, with applications from designing new heterogeneous catalysts for industrial processes to predicting the performance of space vehicles.

Many advances have been made recently in applying Gaussian basis functions in the modelling of the quantum nature of chemical reactions. A typical approach uses overlapping Gaussians that follow likely molecular trajectories as a basis set within which to solve the time dependent Schrödinger equation that describes the quantum behaviour of a molecular system that is undergoing a reaction.

Photosynthesis is the source of all biological solar energy capture, and the source of most atmospheric oxygen. All photosynthetic oxygen production occurs in the oxygen evolving centre of a structure known as photosystem II. However, much remains to be understood about the detailed mechanism of using captured solar energy to generate free charges which go on to oxidise water into oxygen.